#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const double PI = 4 * atan(1);
#define sz(x) (int)(x).size()
#define ll long long
#define ld long double
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define pii pair <int, int>
#define vi vector<int>
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define vpi vector<pair<int, int>>
#define vpd vector<pair<double, double>>
#define pd pair<double, double>
#define f0r(i,a) for(int i=0;i<a;i++)
#define f1r(i,a,b) for(int i=a;i<b;i++)
#define trav(a, x) for (auto& a : x)
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
cout << "["; for(int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]";
}
void fast_io(){
ios_base::sync_with_stdio(0);
cin.tie(NULL);
cout.tie(NULL);
}
void io(string taskname){
string fin = taskname + ".in";
string fout = taskname + ".out";
const char* FIN = fin.c_str();
const char* FOUT = fout.c_str();
freopen(FIN, "r", stdin);
// freopen(FOUT, "w", stdout);
fast_io();
}
const int MAX = 1e5 + 5;
const ll INF = 1e18;
int n, m, s, t, u, v;
vector<pair<int, ll>> adj[MAX];
vi dag[MAX];
vi undo[MAX];
int par[MAX];
vector<ll> use[MAX];
int vis[MAX];
vector<pair<pii, ll>> edges;
int check(int x){
if(use[s][x] + use[t][x] == use[s][t]) return 1;
return 0;
}
void dfs(int src){
vis[src] = 1;
for(auto nxt: adj[src]){
int neigh = nxt.f;
int weight = nxt.s;
if(vis[neigh] == 0 && check(neigh) && weight + use[s][src] == use[s][neigh]){
dag[src].eb(neigh);
dfs(neigh);
}
}
}
vector<ll> dijkstra(int st) {
vector<ll> dist;
f0r(i, n){
dist.eb(INF);
}
dist[st] = 0;
// <distance, <previous vertex, current vertex>>
priority_queue<pair<ll, pair<int, int>>, vector<pair<ll, pair<int, int>> >, greater<pair<ll, pair<int ,int>> > > pq;
pq.emplace(0, make_pair(st, st));
while(!pq.empty()){
auto top = pq.top();
pq.pop();
ll d = top.first;
int prev = top.second.first;
int cur = top.second.second;
if(d > dist[cur])
continue;
par[cur] = prev;
for(auto v: adj[cur]){
int nxt = v.first;
ll w = v.second;
if (dist[nxt] > dist[cur] + w) {
dist[nxt] = dist[cur] + w;
pq.emplace(dist[nxt], make_pair(cur, nxt));
}
}
}
return dist;
}
template<int SZ> struct TopoSort {
int N, in[SZ];
vi res, adj[SZ];
void addEdge(int x, int y) { adj[x+1].pb(y+1), in[y+1] ++; }
bool sort(int _N) {
N = _N; queue<int> todo;
f1r(i,1,N+1) if (in[i] == 0) todo.push(i);
while (sz(todo)) {
int x = todo.front(); todo.pop(); res.pb(x);
trav(i,adj[x]) {
in[i] --;
if (!in[i]) todo.push(i);
}
}
return sz(res) == N;
}
};
TopoSort<MAX> top;
ll dp1[MAX];
ll dp2[MAX];
vi order;
ll ans = INF;
void solve(){
int sz = sz(order);
for(int i: order){
dp1[i] = use[v][i];
for(int nxt: undo[i]){
dp1[i] = min(dp1[i], dp1[nxt]);
}
}
for(int it = sz-1; it>= 0; it--){
int i = order[it];
dp2[i] = use[v][i];
for(int nxt: dag[i]){
dp2[i] = min(dp2[i], dp2[nxt]);
}
}
for(int i: order){
// cout << i << " " << dp1[i] << " " << dp2[i] << " " << use[u][i] << endl;
ans = min(ans, min(dp1[i], dp2[i]) + use[u][i]);
}
}
map<pii, int> um;
int main(){
// io("test");
fast_io;
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
f0r(i, m){
ll ai, bi, ci;
cin >> ai >> bi >> ci;
ai--; bi--;
adj[ai].eb(mp(bi, ci));
adj[bi].eb(mp(ai, ci));
edges.eb(mp(mp(ai, bi), ci));
}
use[s] = dijkstra(s);
use[t] = dijkstra(t);
use[u] = dijkstra(u);
use[v] = dijkstra(v);
for(auto e: edges){
int from = e.f.f;
int to = e.f.s;
ll weight = e.s;
if(check(to) && check(from)){
if(use[s][from] + use[t][to] + weight == use[s][t]){
dag[from].eb(to);
undo[to].eb(from);
top.addEdge(from, to);
}
if(use[s][to] + use[t][from] + weight == use[s][t]){
dag[to].eb(from);
undo[from].eb(to);
top.addEdge(to, from);
}
}
}
top.sort(n);
// cout << top.res << endl;
for(int x: top.res) if(check(x-1)) order.eb(x-1);
solve();
// cout << order << " " << s << " " << t << endl;
// dag_dfs(s, mp(use[u][s], use[v][s]));
ans = min(ans, use[u][v]);
cout << ans << endl;
return 0;
}
